A325718 Number of separable partitions of n in which the number of distinct (repeatable) parts is > 3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 19, 29, 50, 74, 112, 158, 225, 311, 424, 564, 751, 979, 1273, 1638, 2082, 2640, 3323, 4159, 5171, 6419, 7895, 9707, 11872, 14481, 17573, 21319, 25709, 30997, 37205, 44619, 53304, 63646, 75698, 89998, 106664, 126306

Offset: 1

Author

Clark Kimberling, May 17 2019

Keywords

• nonn
• easy

Comments

A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325534 for a guide to related sequences.

Crossrefs

Cf. A000041, A325534.

Programs

Mathematica

(separable=Table[Map[#[[1]]&,Select[Map[{#,Quotient[(1+Length[#]),Max[Map[Length,Split[#]]]]}&,IntegerPartitions[nn]],#[[2]]>1&]],{nn,35}]);
Map[Length[Select[Map[{#,Length[Union[#]]}&,#],#[[2]]>3&]]&,separable]
(* Peter J. C. Moses, May 08 2019 *)

Formula

a(n) = A325534(n) - A325712(n) for n >= 1.